Electromagnetic Radiation – Why Aren’t Graphs for Black Body Radiation Straight Lines? Understanding Thermal Radiation and Wavelength

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We know that a wave which has greater frequency will have low wavelength and high energy. So, by decreasing the wavelength, the frequency and consequently energy (intensity) of that wave will increase or vice versa.

Now, i want to ask a question in black body radiation by looking at the following graphs

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My question is that if by decreasing the wavelength of a wave, the energy of that wave increases then why do these graphs fall down after reaching a maximum value. Shouldn't the graph just move straight on?

Best Answer

You are confusing two very different concepts (but you are certainly not the first) whose biggest connection is that they are both named after Max Planck.

First, there is the energy of a single photon: $$ E = h\nu = \frac{hc}{\lambda}. $$ If you plotted $E$ as a function of $\lambda$, you would indeed get the monotonic relation you seek. This is the Planck relation.

On the other hand, we have the spectrum of light coming from a glowing hot extended object, given either by $$ B_\nu = \frac{2h\nu^3}{c^2(\mathrm{e}^{h\nu/kT}-1)} $$ (for power per unit area per unit frequency) or $$ B_\lambda = \frac{2hc^2}{\lambda^5(\mathrm{e}^{hc/\lambda kT}-1)} $$ (for power per unit area per unit wavelength). This is Planck's Law, which is what you have plotted. These are the distributions of energies (per unit time per unit area) of the many photons emitted from any object that glows (meaning any object above $0~\mathrm{K}$). We call such things spectra. You can divide them by the energy per photon given in the first formula, and thus get the distribution of the number of photons as a function of either frequency or wavelength.